Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

zbMath1461.81031arXiv1901.01984MaRDI QIDQ3298919

Maria V. Perel, I. V. Fialkovsky

Publication date: 16 July 2020

Full work available at URL: https://arxiv.org/abs/1901.01984

zbMATH Keywords

WKB expansionKlein tunnelingLandau-Zener problem

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Asymptotic expansions of solutions to PDEs (35C20) Perturbation theories for operators and differential equations in quantum theory (81Q15) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Quantum dots, waveguides, ratchets, etc. (81Q37)

Related Items (1)

Asymptotics of the Cauchy problem for the one-dimensional Schrödinger equation with rapidly oscillating initial data and small addition to the smooth potential

Cites Work

• Proof of the Landau-Zener formula in an adiabatic limit with small eigenvalue gaps
• Operator separation of variables for adiabatic problems in quantum and wave mechanics
• An asymptotic theory for internal reflection in weakly inhomogeneous elastic waveguides
• Adiabatic perturbation theory in quantum dynamics
• Solutions to the operator equation \(i\varepsilon dy/dt=A(t)y\) on intervals containing turning points
• Nonlinear supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians. I: General properties
• Quantal phase factors accompanying adiabatic changes
• Non-adiabatic crossing of energy levels
• Calculation of correlation function of the director fluctuations in cholesteric liquid crystals by WKB method
• The physics of exceptional points
• Landau–Zener–Stückelberg interferometry in $\mathcal{PT}$-symmetric optical waveguides
• Turning point problems for systems of linear differential equations. Part II: The analytic theory
• On the Connection Formulas and the Solutions of the Wave Equation
• Uniform Asymptotic Formulae for Functions with Transition Points
• Slot Coupling of Rectangular and Spherical Wave Guides
• Turning points for adiabatically perturbed periodic equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings